A simple, yet powerful neural equalizer

The primary objective of this dissertation is the development of a simple and effective method for symbol-by-symbol adaptive equalization capable of tolerating significant levels of distortion in real communication channels.The intent is to maximize equalizer performance, minimize structural complexity and achieve a light computational burden through the adoption of a modified recurrent neural network architecture. The assumed modulation method is bipolar PAM, although the concept should be extensible to more elaborate symbol alphabets.The new structure consists of a single neuron with three inputs and two feedback outputs. Input signal vector components connect through adaptable weights to the neuron nonlinear core or sigmoid. The chosen sigmoid is the hyperbolic tangent function with adaptable slope its argument is the weighted sum of the input vector components. The neuron output or symbol estimate is presented to a slicer whose output provides a binary decision (+1 or --1) for each received symbol.A training period adapts the set of weights as well as the sigmoid slope through a real time approximation of the method of steepest descent with adaptive learning rates proportional to the bit error rate. The algorithm is driven by the error between the desired symbol and the equalizer output in the mean square sense.During the training period the feedback inputs are obtained from the neuron output. At the end of the training sequence, the feedback inputs are obtained from the slicer output.The new structure approximates an unrealizable Bayesian receiver assisted by its fully adaptable set of parameters. Its performance will be shown to be superior to both the linear equalizer and the decision feedback equalizer, as well as to neural equalizers of much larger architectural and computational complexity. The improvement is achieved for most linear and nonlinear channels simulated.A novel theoretical tool is also developed which predicts with remarkable accuracy the achievable bit error rate by the proposed equalizer, under the assumption that the channel impulse response and the signal to noise ratio are known.